Commutative algebra 37 Blowup algebras
This lecture is part of an online course on commutative algebra, following the book
"Commutative algebra with a view toward algebraic geometry" by David Eisenbud.
We survey several different ways of constructing a commutative ring from an increasing or decreasing filtration on a ring. These included blowup or Rees algebras related to blowups in algebraic geometry, graded algebras, and completions. As an application we show how to used graded algebras to show that the (noncommutative) algebra of differential operators over a field of characteristic 0 has no zero divisors, by reducing the question to the corresponding (commutative) graded ring.
Reading: Section 5.1, 5.2
Exercises: 5.1, 5.8